Solution Found!
Consider a random sample X1, X2, ... , Xn from a distribution with pdf f(x; ) = (1 x)1
Chapter 8, Problem 8.6-8(choose chapter or problem)
QUESTION:
Consider a random sample X1, X2, ... , Xn from a distribution with pdf f(x; ) = (1 x)1, 0 < x < 1, where 0 < . Find the form of the uniformly most powerful test of H0: = 1 against H1: > 1.
Questions & Answers
QUESTION:
Consider a random sample X1, X2, ... , Xn from a distribution with pdf f(x; ) = (1 x)1, 0 < x < 1, where 0 < . Find the form of the uniformly most powerful test of H0: = 1 against H1: > 1.
ANSWER:Step 1 of 7
Rewrite the given alternate hypothesis so that the hypothesis is a simple hypothesis on which the Neyman-Pearson lemma can be used.
The hypotheses can be written as,
Since the hypotheses are now simple, the NP lemma can be used.